Effect of polyethylene glycol on the supercoiling free energy of DNA

The supercoiling free energy of pUC19 DNA [2686 base pairs (bp)] was measured in various concentrations of PEG 8000 (polyethylene glycol; molecular weight 8000) by the topoisomer distribution method. The effective twist energy parameter (E(T)) that governs the supercoiling free energy declined linearly by 1.9-fold with increasing w/v % PEG from 0 to 7.5%, which lies below the threshold for intermolecular condensation. In principle, PEG could affect E(T) either via an osmotic exclusion mechanism or by altering the torsion elastic constant, bending rigidity, or self-repulsions of the DNA. Possible alterations of the DNA secondary structure and torsion elastic constant were assessed by CD spectroscopy and time-resolved fluorescence polarization anisotropy of intercalated ethidium. Up to 7.5% PEG, the secondary structure of the DNA remained largely unaltered, as evidenced by (1) the absence of any significant change in the CD spectrum, (2) an extremely small relative decrease (-0.0013) in intrinsic twist, and (3) a negligibly small change in the torsion elastic constant. The observed reduction in E(T) cannot be ascribed primarily to a decrease in torsion elastic constant, and most likely does not stem from a decrease in bending rigidity either. The decrease in medium dielectric constant due to PEG should increase the self-repulsions, and thereby increase E(T), which is opposite to the observed trend. Instead, the observed decline in E(T) is attributed to an osmotic exclusion mechanism. The change in molar volume excluded to the PEG (Delta V(ex)), when the linking difference converts from Delta l = 0 to Delta l = +/-1, was determined from the observed E(T) value and PEG osmotic pressure at each concentration. The experimental Delta V(ex) values agree well with theoretical estimates reckoned for a simple osmotic exclusion model, in which PEG is excluded by hard-core interactions from a concentric cylindrical volume around every duplex segment. The difference in volume excluded to PEG between the Delta l = 0 and the Delta l = +/-1 topoisomers is attributed entirely to the approximately 0.7 additional writhe "crossing" of two duplex strands at roughly 90 degrees, which is known to occur in the latter species. When the separation between the duplex centers at the "crossing" was adjusted so that the theoretical estimate of Delta V(ex) matched the experimental value at each PEG concentration, a value near 5.7 nm was obtained in each case. The invariance and plausible magnitude of this mean separation at the crossing provide strong support for this simple osmotic exclusion model. An alternative model, in which the PEG is excluded from the entire coil envelope of the DNA out to its radius of gyration, perhaps because it decreases the local dielectric constant, was also considered. The estimated difference in excluded volume in that case exceeds the experimental value by a factor of nearly 10(4), and could be ruled out on that basis.

The distribution of end-to-end distances of the weakly bending rod model

The weakly bending rod model is an approximation to a worm-like chain in the limit where the ratio L(0)/P of the contour length L(0) to the persistence length P is not too large. The range of validity of the weakly bending rod model is investigated by deriving analytical expressions for its distribution of end-to-end distances P(L) and its moments <L(m) > and numerically comparing the results with corresponding values for the worm-like chain model. No general, closed form analytical expression for either P(L) or the average length <L> of a worm-like chain exists, so those quantities are obtained by Monte Carlo simulations. Exact analytical expressions for <L(2)> and <L(4)> for the worm-like chain are employed in the comparison of the computed moments. Moments calculated for the approximate distributions of Daniels and Yamakawa and Stockmayer are also compared with the others. In addition, P(L) and its moments for the alternative model of Winkler et al. are compared with the others. The weakly bending rod model gives a reasonably good account of both P(L) and <L(m) >, m = 1,2,4, over the range L(0)/P </= 0.6, but deviates significantly for L(0)/P >/= 1.0. In contrast, the alternative model of Winkler et al. yields rather poor results in the rodlike domain.

The question of long-range allosteric transitions in DNA

The question of long-range allosteric transitions of DNA secondary structure and their possible involvement in transcriptional activation is discussed in the light of new results. A variety of recent evidence strongly supports a fluctuating long-range description of DNA secondary structure. Balanced equilibria between two or more different secondary structures, and the occurrence of very large domain sizes, have been documented in several instances. Long-range allosteric effects stemming from changes in sequence or secondary structure over a small region of the DNA have been observed to extend over distances up to hundreds of base pairs in some cases. The discovery that coherent bending strain beyond a threshold level in small (N < or = 250 base pairs (bp)] circular DNAs significantly alters the DNA secondary structure has important implications, especially for transcriptional activators that either bend the DNA directly or are involved in the formation of DNA loops of sufficiently small size (N < or = 250 bp). Whether the RNA polymerase is activated primarily via protein: protein contacts, as is widely believed, or instead via a bend-induced allosteric transition of the DNA in such a small loop, is now an open question. Binding of the transcriptional activator Sp1 to linear DNA induces a remarkably long-range change in its secondary structure, and catabolite activator protein binding to a supercoiled DNA behaves similarly, though possibly for different reasons. Compelling evidence for a bend-induced long-range structural transmission effect of the transcriptional activator integration host factor on RNA polymerase activity was recently reported. These results may augur a new paradigm in which allosteric transitions of duplex DNA, as well as of the proteins, are involved in the regulation of transcription.

Dynamic bending rigidity of a 200-bp DNA in 4 mM ionic strength: a transient polarization grating study

DNA may exhibit three different kinds of bends: 1) permanent bends; 2) slowly relaxing bends due to fluctuations in a prevailing equilibrium between differently curved secondary conformations; and 3) rapidly relaxing dynamic bends within a single potential-of-mean-force basin. The dynamic bending rigidity (kappa(d)), or equivalently the dynamic persistence length, P(d) = kappa(d)/k(B)T, governs the rapidly relaxing bends, which are responsible for the flexural dynamics of DNA on a short time scale, t < or = 10(-5) s. However, all three kinds of bends contribute to the total equilibrium persistence length, P(tot), according to 1/P(tot) congruent with 1/P(pb) + 1/P(sr) + 1/P(d), where P(pb) is the contribution of the permanent bends and P(sr) is the contribution of the slowly relaxing bends. Both P(d) and P(tot) are determined for the same 200-bp DNA in 4 mM ionic strength by measuring its optical anisotropy, r(t), from 0 to 10 micros. Time-resolved fluorescence polarization anisotropy (FPA) measurements yield r(t) for DNA/ethidium complexes (1 dye/200 bp) from 0 to 120 ns. A new transient polarization grating (TPG) experiment provides r(t) for DNA/methylene blue complexes (1 dye/100 bp) over a much longer time span, from 20 ns to 10 micros. Accurate data in the very tail of the decay enable a model-independent determination of the relaxation time (tau(R)) of the end-over-end tumbling motion, from which P(tot) = 500 A is estimated. The FPA data are used to obtain the best-fit pairs of P(d) and torsion elastic constant (alpha) values that fit those data equally well, and which are used to eliminate alpha as an independent variable. When the relevant theory is fitted to the entire TPG signal (S(t)), the end-over-end rotational diffusion coefficient is fixed at its measured value and alpha is eliminated in favor of P(d). Neither a true minimum in chi-squared nor a satisfactory fit could be obtained for P(d) anywhere in the range 500-5000 A, unless an adjustable amplitude of azimuthal wobble of the methylene blue was admitted. In that case, a well-defined global minimum and a reasonably good fit emerged at P(d) = 2000 A and <deltazeta(2)>(1/2) = 25 degrees. The discrimination against P(d) values <1600 A is very great. By combining the values, P(tot) = 500 A and P(d) = 2000 A with a literature estimate, P(pb) = 1370 A, a value P(sr) = 1300 A is estimated for the contribution of slowly relaxing bends. This value is analyzed in terms of a simple model in which the DNA is divided up into domains containing m bp, each of which experiences an all-or-none equilibrium between a straight and a uniformly curved conformation. With an appropriate estimate of the average bend angle per basepair of the curved conformation, a lower bound estimate, m = 55 bp, is obtained for the domain size of the coherently bent state. Previous measurements suggest that this coherent bend is not directional, or phase-locked, to the azimuthal orientation of the filament.

Manifestations of slow site exchange processes in solution NMR: a continuous Gaussian exchange model

The effects of site exchange due to slow conformational changes in rapidly rotating molecules in solution are examined in detail. Significant gaps in the currently available theory are filled. The effects of site exchange on the lineshape, decay of a simple spin-echo, decay of the even echoes in a Carr-Purcell-Meiboom-Gill (CPMG) pulse-sequence, and decay of the transverse magnetization in a resonant spin-locking field are investigated. Both trajectory and stochastic operator approaches are formulated and shown to be completely equivalent whenever the dynamics of population transfers among the inequivalent sites is governed by either a stationary or a nonstationary Markov process. A nonstationary Markov process may result from Brownian dynamics (a stationary Markov process) in a larger conformational space that contains the subspace of inequivalent sites. A continuous Gaussian exchange model is formulated in which a nucleus undergoes continuous one-dimensional motion in a harmonic potential well that is located in a linear chemical shift gradient. The effects of this Gaussian exchange model on the lineshape, simple spin-echo decay, and decay of the even echoes of a CPMG pulse train are treated rigorously via the trajectory approach. Compact analytical expressions are obtained for the relevant correlation functions in each case. The relevant decays are found to be exponential in the very short time and long time limits, which are not necessarily experimentally significant in any given case. In the fast exchange limit the relevant decays are exponential at all times, and explicit formulas are given for their decay rates. In the long time limit, all discrete multisite models with the same intrinsic Ro2 at every site are shown to be completely equivalent to a continuous Gaussian model with appropriate relaxation time and variance of the Larmor frequency. The effects of this Gaussian exchange model on the decay of the transverse magnetization in a resonant spin-locking field are treated heuristically by a trajectory approach. The intrinsic contribution (Ro1rho) of rapid rotations and dipole-dipole interactions to relax the transverse magnetizations of two nuclei of the same kind in the presence of a (nearly) resonant spin-locking field is also derived and found to be practically the same as the intrinsic contribution, Ro2, of those same rotations to the simple and CPMG spin-echo decay rates and linewidth. Literature data for the linewidth, decay rate of the CPMG even spin-echoes, and R(1rho) decay rate for the A9-H2 protons of adenines at the central TpA step in the sequence, 5'-GCAGGTTTAAACCTCG-3', are analyzed using the Gaussian exchange model to assess the time-scale and variance of the site exchange process as well as the intrinsic Ro2 rate. Although a single Gaussian exchange process with appropriate parameters can fit these three A9-H2 data rather well, this particular "solution" cannot be reconciled with NMR relaxation data on other protons in the same DNA molecule. Rather good agreement with all of the observations is obtained by using a model of two concurrent Gaussian exchange processes, whose relaxation times, tau = 7 and 460 micros, differ in time-scale by a factor of 65. The insensitivity of R1rho in the presence of a fast site exchange process to much slower concurrent site exchange processes is explicitly demonstrated. Protocols for detecting and characterizing a second slow site exchange process are suggested.

Effect of temperature on DNA secondary structure in the absence and presence of 0.5 M tetramethylammonium chloride

Changes in the average secondary structures of three different linear DNAs over the premelting region from 5 to 60 degrees C were investigated by measuring their CD spectra and also their torsion elastic constants (<alpha>) by time-resolved fluorescence polarization anisotropy. For one of these DNAs, the Haell fragment of pBR322, the apparent diffusion coefficients [Dapp(k)] at small and large scattering vectors (k) were also measured by dynamic light scattering. With increasing temperature, all three DNAs exhibited typical premelting changes in their CD spectra, and these were accompanied by 1.4- to 1.7-fold decreases in <alpha>. Also for the 1876 base pair fragment, Dapp(k) at large scattering vectors, which is sensitive to the dynamic bending rigidity, decreased by 17%, even though there was no change at small scattering vectors, where Dapp(k) = D0 is the translational diffusion coefficient of the center-of-mass. These observations demonstrate conclusively that the premelting CD changes of these DNAs are associated with a significant change in average secondary structure and mechanical properties, though not in persistence length. In the presence of 0.5 M tetramethylammonium chloride (TMA-Cl) the premelting change in CD is largely suppressed, and the corresponding changes in <alpha> and Dapp(k) at large scattering vectors are substantially diminished. These observations suggest that TMA-Cl, which binds preferentially to A.T-rich regions and stabilizes those regions (relative to G.C-rich regions) against melting, effectively stabilizes the prevailing low-temperature secondary structure sufficiently that the DNA is effectively trapped in that state over the temperature range observed.

On the origin of the temperature dependence of the supercoiling free energy

Monte Carlo simulations using temperature-invariant torsional and bending rigidities fail to predict the rather steep decline of the experimental supercoiling free energy with increasing temperature, and consequently fail to predict the correct sign and magnitude of the supercoiling entropy. To illustrate this problem, values of the twist energy parameter (E(T)), which governs the supercoiling free energy, were simulated using temperature-invariant torsion and bending potentials and compared to experimental data on pBR322 over a range of temperatures. The slope, -dE(T)/dT, of the simulated values is also compared to the slope derived from previous calorimetric data. The possibility that the discrepancies arise from some hitherto undetected temperature dependence of the torsional rigidity was investigated. The torsion elastic constant of an 1876-bp restriction fragment of pBR322 was measured by time-resolved fluorescence polarization anisotropy of intercalated ethidium over the range 278-323 K, and found to decline substantially over that interval. Simulations of a 4349-bp model DNA were performed using these measured temperature-dependent torsional rigidities. The slope, -dE(T)/dT, of the simulated data agrees satisfactorily with the slope derived from previous calorimetric measurements, but still lies substantially below that of Duguet's data. Models that involve an equilibrium between different secondary structure states with different intrinsic twists and torsion constants provide the most likely explanation for the variation of the torsion constant with T and other pertinent observations.

Comparison of hard-cylinder and screened Coulomb interactions in the modeling of supercoiled DNAs

A 1000 base pair (bp) model supercoiled DNA is simulated using spherical screened Coulomb interactions between subunits on one hand and equivalent hard-cylinder interactions on the other. The amplitudes, or effective charges, of the spherical screened Coulomb electrostatic potentials are chosen so that the electrostatic potential surrounding the middle of a linear array of 2001 subunits (31.8 A diameter) closely matches the solution of the nonlinear Poisson-Boltzmann equation for a cylinder with 12 A radius and the full linear charge density of DNA at all distances beyond the 24 A hard-core diameter. This superposition of spherical screened Coulomb potentials is practically identical to the particular solution of the cylindrical linearized Poisson-Boltzmann equation that matches the solution of the nonlinear Poisson-Boltzmann equation at large distances. The interaction energy between subunits is reckoned from the effective charges according to the standard DLVO expression. The equivalent hard-cylinder diameter is chosen following Stigter's protocol for matching second virial coefficients, but for the full linear charge density of DNA. The electrostatic persistence length of the model with screened Coulomb interactions is extremely sensitive to the (arbitrarily) chosen subunit length at the higher salt concentrations. The persistence length of the hard-cylinder model is adjusted to match that of the screened Coulomb model for each ionic condition. Simulations for a superhelix density sigma = -0.05 using a spherical screened Coulomb interaction plus a 24 A hard-cylinder core (SCPHC) potential indicate that the radius of gyration of this 1000 bp DNA actually undergoes a slight increase as the NaCl concentration is raised from 0.01 to 1.0M. Thus, merely softening the potential from hard-cylinder to screened Coulomb form does not produce a large decrease in radius of gyration with increasing NaCl concentration for DNAs of this size. Radii of gyration, static structure factors, and diffusion coefficients obtained using the equivalent hard-cylinder (EHC) potential agree well with those obtained using the SCPHC potential in 1.0M NaCl, but in 0.1M NaCl the agreement is not as good, and in 0.01M NaCl the agreement is definitely unsatisfactory. These conclusions differ in significant respects from those obtained in previous studies.

Effects of Na+ and Mg2+ on the structures of supercoiled DNAs: comparison of simulations with experiments

Recent cryo-electron microscopy (cryo-EM) results suggest that sufficient NaCl concentration (> or approximately 0.1 M) and superhelix density (> or approximately-0.05) cause circular DNAs to adopt highly extended, tightly interwound configurations, in which the strands are laterally contiguous along almost their entire length. Millimolar levels of MgCl2 reportedly act synergistically with NaCl to produce similar conformations. However, Monte Carlo simulations with purely repulsive interduplex forces failed to reproduce such structures. In the present work, solution measurements of particular physical properties were performed both to characterize the effects of Na+ and Mg2+ on DNA structure and to provide quantitative tests of Monte Carlo simulations of circular DNAs. Supercoiled p30 delta DNAs in 10 mM Tris plus 0, 0.122, and 0.1 M NaCl, and 0.1 M NaCl plus 4 mM Mg2+ were examined by static and dynamic light scattering (LS and DLS), time-resolved fluorescence polarization anisotropy (FPA) of intercalated ethidium, and circular dichroism (CD) spectroscopy. Upon addition of 0.122 M NaCl, the radius of gyration (Rg) decreased substantially, which indicates that p30 delta adopts a more compact structure. This contradicts the cryo-EM studies, where molecular extension and Rg both increase upon adding 0.1 M NaCl. In 0.1 M NaCl, the torsion constant measured by FPA is practically invariant to superhelix density, and the plateau diffusion coefficient at large scattering vector (Dplat) is likewise nearly the same at both relaxed and native superhelix densities. Such invariance is difficult to reconcile with any transition from relaxed circles to tightly interwound structures with laterally contiguous strands. Metropolis Monte Carlo simulations were performed to generate canonically distributed sets of structures, from which average Do values and scattered intensity ratios, [symbol: see text]I (zero) [symbol: see text]/[symbol: see text] l(k) [symbol: see text], were calculated. Agreement between simulations and experiments in regard to [symbol: see text] I(O) [symbol: see text] /[symbol: see text] I(k) [symbol: see text], D(zero) and the supercoiling free energy, delta Gsc (delta l), is remarkably good for the most extensively studied p30 delta samples. The simulated structures exhibit no sign of very tight interwinding with extensive lateral contacts, but instead exhibit most probable superhelix diameters of 85 to 90 A. When 4 mM Mg2+ was added to native supercoiled p30 delta in 0.1 M NaCl, Rg decreased, D(zero) increased, and the longest internal relaxation rate (1/tau 2(zero)) increased, all of which indicate a further overall contraction of the molecular envelope. The torsion constant exhibited a slight increase that is hardly statistically significant. In this case, agreement between the simulations and experiments was only semi-quantitative for most samples investigated, although the predicted contraction was exhibited by all five samples of p30 delta and one of pBR322 DNA. The simulated structures in 0.1 M NaCl plus 4 mM Mg2+ again showed no sign of extensive lateral contacts. A plausible explanation is proposed for the highly extended, tightly interwound structures seen in cryo-EM, and explicitly tested by Monte Carlo simulations of a 1000 bp circular DNA at +25 and -50 degrees C. Structures identical to those seen in cryo-EM are in fact the equilibrium structures in the simulations at -50 degrees C, and the estimated time for equilibration (2.3 x 10(-6) second) is much smaller than the estimated time for vitrification (1 x 10(-4) second).

Effect of bending strain on the torsion elastic constant of DNA

The torsion constants of both circular and linear forms of the same 181 bp DNA were investigated by time-resolved fluorescence polarization anisotropy (FPA) of intercalated ethidium. The ratio of intrinsic ethidium binding constants of the circular and linear species was determined from the relative fluorescence intensities of intercalated and non-intercalated dye in each case. Possible changes in secondary structure were also probed by circular dichroism (CD) spectroscopy. Upon circularization, the torsion constant increased by a factor of 1.42, the intrinsic binding constant for ethidium increased by about fourfold, and the CD spectrum underwent a significant change. These effects are attributed to an altered secondary structure induced by the bending strain. Quantitative agreement between torsion constants obtained from the present FPA studies and previous topoisomer distribution measurements on circular DNAs containing 205 to 217 bp removes a long-standing apparent discrepancy between those two methods. After storage at 4 degrees C for eight months, the torsion constant of the circular DNA increased by about 1.25-fold, whereas that of the linear DNA remained unchanged. For these aged circles, both the torsion constant and intrinsic binding constant ratio lie close to the corresponding values obtained previously for a 247 bp DNA by analyzing topoisomer distributions created in the presence of various amounts of ethidium. The available evidence strongly implies that torsion constants measured for small circular DNAs with less than 250 bp are specific to the altered secondary structure(s) therein, and are not applicable to linear and much larger circular DNAs with lower mean bending strains.

Thermodynamics of the first transition in writhe of a small circular DNA by Monte Carlo simulation

Monte Carlo simulations are employed to investigate the thermodynamics of the first transition in writhe of a circular model filament corresponding to a 468 base-pair DNA. Parameters employed in these simulations are the torsional rigidity, C = 2.0 x 10(-19) dyne cm2, and persistence length, P = 500 A. Intersubunit interactions are modeled by a screened Coulomb potential. For a straight line of subunits this accurately approximates the nonlinear Poisson-Boltzmann potential of a cylinder with the linear charge density of DNA. Curves of relative free energy vs writhe at fixed linking difference (delta l) exhibit two minima, one corresponding to slightly writhed circles and one to slightly underwrithed figure-8's, whenever delta l lies in the transition region. The free energies of the two minima are equal when delta lc = 1.35, which defines the midpoint of the transition. At this midpoint, the free energy barrier between the two minima is found to be delta Gbar = (0.20) kBT at 298 K. Curves of mean potential energy vs writhe at fixed linking difference similarly exhibit two minima for delta l values in the transition region, and the two minimum mean potential energies are equal when delta l = 1.50. At the midpoint writhe, delta lc = 1.35, the difference in mean potential energy between the minimum free energy figure-8 and circle states is (1.3) kBT, and the difference in their entropies is 1.3 kB. Thus, the entropy of the minimum free energy figure-8 state significantly exceeds that of the circle at the midpoint of the transition. The first transition in writhe is found to occur over a rather broad range of delta l values from 0.85 to 1.85. The twist energy parameter (ET), which governs the overall free energy of supercoiling, undergoes a sigmoidal decrease, while the translational diffusion coefficient undergoes a sigmoidal increase, over this same range. The static structure factor exhibits an increase, which reflects a decrease in radius of gyration associated with the circle to figure-8 transition.

Effect of anisotropy of the bending rigidity on the supercoiling free energy of small circular DNAs

In principle, the supercoiling free energy of a small circular DNA will be enhanced by increasing the anisotropy of its bending potential at constant persistence length. The magnitude of this effect is investigated by Monte Carlo simulation using an extension of a previously proposed algorithm. The supercoiling free energy at 298 K is simulated for circular DNAs containing N = bp with torsion constant alpha = 5.8 X 10(-12) dyne cm, persistence lengths P = 500 A and 10,000 A, and a range of anisotropies of the bending potential from rho = 1.0 to 16.0. The apparent torsion constants, reckoned from these supercoiling free energies by assuming an isotropic bending potential, are found to increase by less than 3% as the input anisotropy increases from 1.0 to 16.0 When P = 500 A, the apparent torsion constant never rises significantly above the input value over the entire range of input anisotropies. When P = 10,000 A, the apparent torsion constant rises only about 3% above the input value for anisotropies rho = 8.0 and 16.0. Evidently, anisotropy of the bending potential cannot account for the fact that the torsion constants reported for small circular DNAs exceed those reported for long linear DNAs by a factor of 1.6 or more.

Monte Carlo simulations of supercoiling free energies for unknotted and trefoil knotted DNAs

A new Monte Carlo (MC) algorithm is proposed for simulating inextensible circular chains with finite twisting and bending rigidity. This new algorithm samples the relevant Riemann volume elements in a uniform manner, when the constraining potential vanishes. Simulations are performed for filaments comprising 170 subunits, each containing approximately 28 bp, which corresponds to a DNA length of 4770 bp. The bending rigidity is chosen to yield a persistence length, P = 500 A, and the intersubunit potential is taken to be a hard-cylinder potential with diameter d = 50 A. This value of d yields the same second virial coefficient as the electrostatic potential obtained by numerical solution of the Poisson-Boltzmann equation for 150 mM salt. Simulations are performed for unknotted circles and also for trefoil knotted circles using two different values of the torsional rigidity, C = (2.0 and 3.0) x 10(-19) dyne cm2. In the case of unknotted circles, the simulated supercoiling free energy varies practically quadratically with linking difference delta l. The simulated twist energy parameter ET, its slope dET/dT, and the mean reduced writhe <w>/delta l for C = 3 x 10(-19) dyne cm2 all agree well with recent simulations for unknotted circles using the polygon-folding algorithm with identical P, d, and C. The simulated ET vs. delta l data for C = 2.0 x 10(-19) dyne cm2 agree rather well with recent experimental data for p30 delta DNA (4752 bp), for which the torsional rigidity, C = 2.07 x 10(-19) dyne cm2, was independently measured. The experimental data for p30 delta are enormously more likely to have arisen from C = 2.0 x 10(-19) than from C = 3.0 x 10(-19) dyne cm2. Serious problems with the reported experimental assessments of ET for pBR322 and their comparison with simulated data are noted. In the case of a trefoil knotted DNA, the simulated value, (ET)tre, exceeds that of the unknotted DNA, (ET)unk, by approximately equal to 1.40-fold at magnitude of delta l = 1.0, but declines to a plateau about 1.09-fold larger than (ET)unk when magnitude of delta l > or = 15. Although the predicted ratio, (ET)tre/(ET)unk approximately equal to 1.40, agrees fairly well with recent experimental measurements on a 5600-bp DNA, the individual measured ET values, like some of those reported for pBR322, are so large that they cannot be simulated using P = 500 A, d = 50 A, and any previous experimental estimate of C.

Position-dependent internal motions and effective correlation times for magnetization transfer in DNA

An effective correlation time that accounts for position dependence of the combined local angular motions and collective twisting and bending deformations, as well as for anisotropic uniform rotation, is defined in terms of the magnetization-transfer rate and expressed in terms of molecular parameters. Application to measured magnetization-transfer rates from H6 to H5 of cytosine in cases where all other relevant data, including the uniform rotational diffusion coefficients, are known, suggests that the amplitude of local angular motion, as well as that due to collective deformations, is significantly greater for a penultimate base pair than for base pairs near the center of the molecule, and that such amplitudes might be approximately transferable from one molecule to another. Protocols are suggested for using estimated ratios of effective correlation times in the initial calibrations of internuclear distances and in the subsequent structure-refinement process.

A test of the model-free formulas. Effects of anisotropic rotational diffusion and dimerization

The effects of anisotropy of rotational diffusion and extent of dimerization on the performance of the simple and extended model-free formulas are investigated. Numerically exact 15N NMR R1, R2, and NOE data are simulated for cylindrically symmetric species and also for mixtures of spherical monomers and dimers with the same internal dynamics. The relevant internuclear vectors are assumed to move in isotropic deflection potentials fixed at different orientations in the molecule and to exhibit a single relaxation time in their internal correlation functions. The simple model-free formula is fitted to these simulated data in order to obtain the best-fit order parameter and internal relaxation time for each nucleus. Fitting is accomplished by the standard data-analysis protocol, in which a single common global correlation time is adjusted, and also by an alternative protocol, in which the global correlation time is adjusted separately for each nucleus. The extended model-free formula is likewise fitted to these same data. With noise-free data, the simple model-free formula and standard protocol yield remarkably good best-fit internal motion parameters up to moderate anisotropies (r = D parallel/D perpendicular = 2.0), but some or many of the NMR relaxation data are not fitted well even for quite modest anisotropies (r = 1.3). The extended model-free formula yields an improved fit to the NMR data, but predicts substantial amplitudes of nonexistent slow internal motions (tau approximately greater than 0.2 ns) for many of the nuclei for all r > or = 1.3. The simple model-free formula with the alternate protocol yields even better internal motion parameters than the standard protocol and also an excellent fit to the NMR relaxation data. The best-fit global correlation time for each nucleus corresponds very closely to the theoretical correlation time defined herein. Knowledge of these times would allow one not only to estimate the anisotropy of diffusion but also in favorable cases to infer the existence of slow internal motions. Inclusion of typical statistical errors in R1, R2, and NOE, or modest exchange contributions to R2, seriously degrades the performance of the simple model-free formula with either protocol, especially in regard to the internal relaxation times, which can exhibit very large deviations from their input value even for spherical diffusors. When the fraction of monomers existing as dimers lies in the range 0.1 < or = fd < or = 0.8, none of the three model-free approaches tested yields reliable internal motion parameters.

Effect of ethidium binding and superhelix density on the supercoiling free energy and torsion and bending constants of p30 delta DNA

Topoisomer distributions created by the action of topoisomerase I on p30 delta DNA in the presence of various concentrations of ethidium are measured and analyzed using recently developed theory to obtain the twist energy parameter (ET) that governs the free energy of supercoiling in each case. Competitive dialysis experiments to investigate the relative affinity of ethidium for linear and supercoiled DNAs at different binding ratios are assayed fluorometrically and the results are analyzed using related theory. The topoisomer distributions and fluorescence intensity ratios agree well with the theory, which is based on the assumption that the supercoiling free energy varies quadratically with the effective linking difference, regardless of ethidium binding or superhelix density. The topoisomer distribution experiments alone yield an average best-fit value, ET = 950 +/- 80, independent of ethidium binding ratio from r = 0 to 0.082, while the combined topoisomer distribution and ethidium binding experiments yield an average best-fit value, ET = 1030 +/- 90, which is essentially independent of ethidium binding ratio from r = 0 to 0.082 and superhelix density from sigma = 0 to (-)0.053. One may conclude that the supercoiling free-energy-varies quadratically with effective linking difference over the entire range of observed ethidium binding ratios and superhelix densities. The independently measured torsion constant (alpha) of p30 delta DNA is likewise essentially independent of superhelix density and ethidium binding ratio. The observed invariance of ET and alpha implies that the bending constant kappa beta is similarly invariant to superhelix density and ethidium binding ratio. The apparently ideal behavior displayed by p30 delta DNA is not exhibited by pBR322 DNA, which is discussed in the following companion paper.

A model for the binding of E. coli single-strand binding protein to supercoiled DNA

A model is proposed for the binding of E. coli single strand binding protein (SSB) to supercoiled DNA. The basic tetrameric binding units of SSB are assumed to bind in pairs to the complementary single strands of a locally melted region. The cooperativity of the binding includes contributions from both protein-protein and base-pair stacking interactions. Each bound SSB tetramer is assumed to unwind l = 34 bp, which implies an unwinding angle of 3.27 turns. The resulting loss of superhelical strain is the essential driving force for binding SSB to supercoiled DNAs. All molecular parameters entering into the theory are estimated from available data, except for the composite binding constant (Ka), which is adjusted to best-fit the theory to the fluorescence quenching (FQ) and diffusion coefficient (D0) data of Langowski et al. Very good fits are obtained with optimum values of Ka that are consistent with estimates from other data. This binding model predicts several noteworthy features. (1) SSB binds essentially always in a single contiguous stack on a supercoiled plasmid, and relative fluctuations in stack length are quite small, in agreement with results of electron microscopy studies. (2) The progressive loss of superhelical strain with increasing bound ligand decreases the affinity of the DNA for SSB. This anti-cooperativity offsets the cooperativity of the binding and causes apparent saturation of the binding at rather low binding ratios. Consequently, over the limited span of the measurements, the FQ data can also be satisfactorily fitted by a non-cooperative model comprising a small number of independent sites. (3) When SSB binds to a population of different topoisomers, the distribution of linking differences of the resulting complexes is extremely narrow. Thus, SSB acts to level any differences in superhelical strain in a population of topoisomers. Finally, the effects of restricting binding to a region comprising only part of the plasmid are assessed.

Effect of ethidium binding and superhelix density on the apparent supercoiling free energy and torsion constant of pBR322 DNA

The value of the twist energy parameter (ET) of pBR322 is determined near zero superhelix density from topoisomer distributions created under various conditions. The resulting value, ET = 1155 +/- 65, at 37 degrees C is essentially unaffected by adding 10 mM Mg2+, or by changing the kind of Topo I from chicken-red-cell to calf-thymus. This value significantly exceeds that (ET = 950 +/- 80) measured for p30 delta DNA under identical conditions by the same method in the preceding paper. Decreasing the temperature from 37 to 21 degrees C yields a slightly larger value, ET = 1340 +/- 130, but the statistical significance of the increase is marginal. Attempts to determine reliable ET values for pBR322 at higher superhelix densities by ethidium binding were frustrated by the fact that good fits of the equilibrium dialysis results could not be achieved using a single value of ET. Moreover, the curves of apparent ET versus binding ratio r vary considerably from one preparation to another, and for a given preparation vary with time after cell lysis up to about seven weeks, after which they settle in to nearly reproducible behavior. The apparent ET values obtained from competitive dialysis experiments are typically rather low (ET approximately 700) for small r and nearly native superhelix density, and rise up to 1300 to 1500 with increasing binding ratio (up to r = 0.055) and decreasing negative superhelix density.(ABSTRACT TRUNCATED AT 250 WORDS)

Circularization of small DNAs in the presence of ethidium: a theoretical analysis

A rigorous theory is developed for ethidium binding to linear and circular DNAs and for the ratios of topoisomers produced upon ligation of an equilibrium population of noncovalently closed circles in the presence of ethidium. Assuming an unwinding angle theta E = 26 degrees for intercalated ethidium, optimum values of the intrinsic binding constant, KE = 7.16 x 10(4) M-1, the intrinsic twist, l0 = 23.746 turns, and twist energy parameter, Et = 5250, are obtained by fitting the present theory to the data of Shore and Baldwin [(1993) Journal of Molecular Biology, Vol. 170, pp. 983-1007] for a 247 base pair DNA. A very good fit is achieved with these optimum values, but a poor fit results when the parameters estimated by Shore and Baldwin are employed in the same theory. Three assumptions employed in the analysis of Shore and Baldwin are found to be not strictly valid. Adoption of the present substantially larger Et value as representative of their short DNAs would allow the Et vs N data of Shore and Baldwin to conform to the shape predicted by Shimada and Yamakawa [(1985) Journal of Molecular Biology, Vol. 184, pp. 319-329] and Frank-Kamenetskii et al. [(1985) Journal of Biomolecular Structure and Dynamics, Vol. 2, pp. 1005-1012], and would imply that all of their DNAs exist in a substantially stiffer than normal state.

Effects of different cations on the hydrodynamic radius of DNA

The effects of different cations on the hydrodynamic radius (RH) of a 48-bp synthetic DNA are measured by time-resolved fluorescence polarization anisotropy of intercalated ethidium. Relative statistical errors in RH are only approximately 1%. With increasing cation concentration, Na+ causes a small decrease in RH, Cs+ causes a somewhat larger decrease by up to 0.5 A at 100 mM, and (CH3CH2)4N+ causes an increase in RH by approximately 0.5 A at 100 mM. The qualitatively different effects of these monovalent cations indicates that the changes in RH with cation concentration do not arise primarily from electrolyte friction. Divalent cations cause much larger increases in RH with increasing cation concentration. Mg2+ causes an increase in RH by up to 1.0 A at 24.4 mM, and Mn2+ causes an increase in RH by up to 1.6 A at 24.4 mM. These effects are independent of DNA concentration. There is some positive correlation between the order of effects of the different cations on RH and the order of their effects on interhelical hydration forces. It is suggested that these different ions affect RH either by altering the hydration layer or possibly by some effect on DNA structure, such as stabilizing bends.

The amplitude of local angular motion of purines in DNA in solution

Nuclear magnetic resonance and optical experiments are combined to determine the rms amplitude of local angular motion of purines in DNA in solution. A 12 base-pair duplex DNA with the sequence d(CGCGAATTCGCG)2 is deuterated at the H8 positions of adenine and guanine by exchange with solvent at 55 degrees C. The deuterium nmr spectrum of this DNA is measured at 30 mg/mL at 30 degrees C in an 11.76 Tesla magnet (76.75 MHz). The time-resolved fluorescence polarization anisotropies (FPA) of this same sample and also a greatly diluted sample (0.215 mg/mL) were measured after addition of ethidium. FPA measurements of the dilute sample yield the hydrodynamic radius, RH = 9.94 +/- 0.2 A, while those at the nmr concentration are employed to characterize the collective motions in terms of either an enhanced viscosity or dimer formation. The rms amplitude of local angular motion was determined by analyzing the 2H-nmr spectrum, in particular the line width, using recently developed theory for the transverse relaxation rate (RQ2) together with essential information about the collective motions from these and other optical studies. When the principal-axis frame of the electric field gradient tensor is assumed to undergo overdamped libration around each of its three body-fixed axes in an isotropic deflection potential, then the rms amplitude of local angular motion around any single axis is found to lie in the range 10 degrees-11 degrees, provided the high DNA concentration acts to enhance the viscosity, and is about 9 degrees-11 degrees, if it acts to produce end-to-end dimers. The proton nmr relaxation data of Eimer et al. are reanalyzed and shown to yield an rms amplitude of angular motion of the cytosine H5-H6 internuclear vector of 9 degrees-10 degrees, depending upon its orientation with respect to the helix axis. In all of these analyses, full account is taken of the collective twisting and bending deformations, which have a small but significant effect on the results. It is shown that the rms amplitudes of local angular motion do not depend strongly on the model (potential), provided that isotropic rotation around the same number of axes is allowed and that one compares rms angles of the same dimensionality. The rms amplitudes of local angular motion in solution are comparable to those observed for the same sequence at low levels of hydration in the solid state.

Dynamics and structures of DNA: long-range effects of a 16 base-pair (CG)8 sequence on secondary structure

The effects of inserting 16 base pair (bp) of alternating CG [(CG)8] near the middle of a much longer restriction fragment (1097 bp) are investigated by measuring various properties that are sensitive to secondary and tertiary structure. Results for this fragment are compared with those for a control fragment (1089 bp) with the identical sequence except at the insert. Another fragment (1382 bp), which contains a 296-bp extension at the 5'-end of the 1089-bp control fragment, is also used as a secondary control in some experiments. When the 1097-bp (CG)8 insert fragment is compared with the control fragments in 0.1 M NaCl buffer, the (CG)8 insert is found to induce disproportionately large relative changes in the molar ellipticity at 273 nm ([theta]273), the torsion constant (alpha) measured by fluorescence polarization anisotropy, the optical melting profile, and the susceptibility to S1 nuclease. Estimates of the minimum distance over which the (CG)8 insert alters the secondary structure range from 330 to 550 bp. With increasing NaCl concentration, the 1097-bp insert fragment undergoes a structural transition between 2.0 and 2.5 M that is manifested in the apparent diffusion coefficient (Dplat) from dynamic light scattering at large scattering vector. This transition, which is not exhibited by the control DNAs, is presumed to involve formation of Z-helix at the insert. However, the observed decrease in (Dplat) is attributed to an increase in bending rigidity, which perforce must be globally distributed far beyond the (CG)8 insert per se. In 4.25 M NaCl (but not in 0.1 M NaCl), the addition of 1 ethidium dye per 300 bp induces an extensive structural transition in the 1097 bp (CG)8 insert fragment. This transition, which also is not exhibited by the control DNAs, significantly decreases the bending rigidity, doubles [theta]273, and takes place on a time scale of a few days. Removal of ethidium and salt by dialysis vs 0.1 M NaCl buffer restores the original properties of the 1097-bp (CG)8 insert fragment. The present results are consistent with a (fluctuating, long-range) description of the secondary structure in which a given short sequence transiently fluctuates among two or more distinct secondary structures that extend over much larger domains of variable position and size, and whose relative stabilities depend on distant as well as close-lying base pairs.

Effect of ethidium on the torsion constants of linear and supercoiled DNAs

The torsion elastic constants (alpha) of linear pBR322 (4363 bp) and pUC8 (2717 bp) DNAs and supercoiled pBR322 and pJMSII (4375 bp) DNAs are measured in 0.1 M NaCl as a function of added ethidium/base-pair (EB/BP) ratio by studying the fluorescence polarization anisotropy (FPA) of the intercalated ethidium. The time-resolved FPA is measured by using a picosecond dye laser for excitation and time-correlated single photon counting detection. Previously developed theory for the emission anisotropy is generalized to incorporate rotations of the transition dipole due to excitation transfer. The excitation transfers are simulated by a Monte Carlo procedure (Genest et al., Biophys. Chem. 1 (1974) 266-278) and the consequent rotations of the transition dipole are superposed on the Brownian rotations. After accounting for excitation transfer, the torsion constants of the linear DNAs are found to be essentially independent of intercalated ethidium up to a binding ratio r = 0.10 dye/bp. Dynamic light scattering measurements on linear pUC8 DNA confirm that the torsion constant is independent of binding ratio up to r = 0.20 dye/bp. If alpha d denotes the torsion constant between ethidium and a base-pair, and alpha 0 that between two base-pairs, then our data imply that alpha d/alpha 0 lies in the range 0.65 to 1.64 with a most probable value of 1.0. The torsion constants of supercoiled DNAs decrease substantially with increasing binding ratio even after accounting for excitation transfer. At the binding ratio r* = 0.064, where the superhelix density vanishes and superhelical strain is completely relaxed, the torsion constant of the supercoiled pBR322 DNA/dye complex lies below that of the corresponding linear DNA/dye complex by about 30%. This contradicts the conventional view according to which linear, nicked circular, and supercoiled DNA/dye complexes with r = r* should coexist with the same concentration of free dye, display the same distribution of bound dye, and exhibit identical secondary structures, twisting and bending rigidities, and FPA dynamics. These and other observations imply the existence of metastable secondary structure in freshly relaxed supercoiled DNAs. A tentative explanation is presented for these and other unexpected observations on supercoiled DNAs.

Dynamic light scattering from weakly bending rods: estimation of the dynamic bending rigidity of the M13 virus

A theory is presented for the dynamic structure factor [S(K,t]) of weakly bending rods. This treatment is based on a discrete bead model for the Brownian dynamics in which all bead motions associated with bending are constrained to occur in a plane perpendicular to the end-to-end vector, thus prohibiting extension or contraction along that axis. Preset hydrodynamic interactions are incorporated in a numerically exact manner. The predicted normalized dynamic structure factor S(K,t)/S(K,0) should be valid for short times t such that the rms rotation of the end-to-end vector around any transverse axis is much less than 1.0 radian. With geometrical parameters appropriate for the M13 virus, the intensity autocorrelation function G(2) (K,t) = 1 + magnitude of S(K,t)/S(K,0)2 is calculated over a range of times and scattering vectors K for selected values of the persistence length P. The calculated G(2) (K,t) are fitted to a single exponential with unit baseline over the same range of times as the experimental photon correlation functions, and the apparent diffusion coefficients Dapp (K) are obtained from the best-fit relaxation times. For the sake of completeness, an exact expression is derived for the apparent diffusion coefficient obtained from the initial slope of the dynamic structure factor. However, this does not reduce to the known correct result in the rigid rod limit. To obtain the correct result, the limit of infinite bending rigidity must be taken before the limit of zero time. For this and other reasons, the initial slope value of Dapp (K) is not useful for weakly bending rods. Photon correlation functions are measured for the M13 virus, which is virtually identical to the often-studied fd virus. The experimental photon correlation functions are fitted over 8 relaxation times to a single-exponential plus baseline, and the Dapp (K) are calculated from the best-fit relaxation times. Theoretical curves of Dapp (K) vs K2 for selected values of P are compared with the experimental data, which are satisfactorily reproduced when P = 22000 +/- 2000 A. This dynamic value is close to the static value, P = 20000 +/- 2000 A, reported for the very similar fd virus. The most recent theories of Maeda and Fujime and their dynamic light scattering studies of fd virus are compared with the present results in some detail. Their optimum value of P is in surprisingly good agreement with the present value.

Evidence for allosteric transitions in secondary structure induced by superhelical stress

Previous studies suggest that the global secondary structures of native supercoiled and equilibrium linear DNAs may differ somewhat. Recent evidence also indicates that metastable secondary structure commonly persists following complete relaxation of the superhelical stress by intercalating dyes or by the action of topoisomerase I. In this work, the torsion constants (alpha) of pBR322, pUC8 and M13mp7 (replicative form) DNAs are determined by time-resolved fluorescence polarization anisotropy at various times subsequent to linearization. In all three cases, the torsion constants are relatively low immediately after linearization, and evolve for eight to ten weeks before reaching their apparent equilibrium values. It is shown in detail how the persistence of metastable secondary structure, subsequent to relaxation of superhelical stress, necessarily implies that one or more transitions in equilibrium secondary structure are induced as the superhelix density is varied from zero to native, or vice versa. Samples of pUC8 dimer (5434 base-pairs) with different superhelix densities are prepared by the action of topoisomerase I in the presence of various amounts of ethidium. Their median linking number differences are determined by standard band counting methods. The translational diffusion coefficient (Do) and the plateau diffusion coefficient (Dplat) characterizing internal motions over short distances (225 A) are determined by dynamic light-scattering. The torsion constant (alpha) between base-pairs and the circular dichroism spectrum are also measured for each sample. Curves of Dplat, Do, alpha and molar ellipticity ([theta]) (at the minimum near 250 nm) versus superhelix density (sigma) are constructed. The curve of Do versus sigma is very similar to that for sedimentation coefficient versus sigma for simian virus 40 (SV40) and polyoma DNAs. The curves of Dplat, Do, alpha and [theta] versus sigma show that, with increasing negative superhelix density, a structural transition occurs near sigma = -0.020 to an intermediate state with low torsion constant, and a second structural transition occurs near sigma = -0.035 to a state that exhibits more normal properties by sigma = -0.048. These data are consistent with the hypothesis that supercoiling induces two successive allosteric transitions to alternative global secondary structures. The data are much less consistent with the hypothesis that supercoiling induces some radical secondary structure at one or a few sites of small extent at sigma = -0.020, and at other sites at sigma = -0.035, or with hypotheses based on changes in tertiary structure alone.(ABSTRACT TRUNCATED AT 400 WORDS)

Intramolecular interference effects in dynamic light scattering: rigid double spirals and superhelical DNAs

A theory is developed for dynamic light scattering (DLS) from rigid double spirals by treating an invisible rigid cylinder with two helical scattering stripes on opposite sides of its cylindrical surface. The exact initial, or first cumulant, diffusion coefficient Dapp (K) is obtained in terms of the translational diffusion coefficients (D parallel and D perpendicular) parallel and perpendicular to the symmetry axis, the rotational diffusion coefficients (DR parallel and DR perpendicular) around the symmetry and transverse axes, the length (L) and radius (b) of the cylindrical surface bearing the stripes, and the pitch (p). Interference effects, namely geometrical antiresonances, between strands, produce deep minima in the static structure factor S (K) and corresponding prominent peaks in Dapp (K). These peaks in Dapp (K) depend sensitively on the rotational dynamics around the symmetry axis, and nearly vanish when DR parallel = 0. Some results for single spirals are also presented. A simpler model in which scattering points are attached at opposite ends of an otherwise invisible thin rigid rod is also treated, and shown to exhibit modest minima in S (K) and corresponding maxima in Dapp (K). Confining this rod to a plane containing K enhances the amplitudes of the oscillations in S (K) and Dapp (K), as expected. Rigid double spirals are employed as crude models for interwound supercoiled DNAs in order to assess the possible occurrence of interference effects. Although native supercoiled DNAs exhibit a cylinder diameter that is much too small to exhibit geometrical antiresonances in the presently accessible range of K2, nearly relaxed supercoiled DNAs are predicted to exhibit their first maximum in Dapp (K) just inside this range. Previously reported data for the effect of Escherichia coli single-strand binding (ssb) protein on the DLS of supercoiled pBR322 DNA cannot be mimicked by a gradual homogeneous reduction of superhelix density with increasing ssb, but instead can be mimicked by inhomogeneous all-or-none binding in which uncomplexed native DNAs and nearly relaxed saturated ssb/DNA complexes coexist in varying proportions. Experimental Dapp (K) and S (K) data for a sample of relaxed pUC8 dimers display, respectively, a broad maximum and a corresponding minimum, in qualitative agreement with rough theoretical predictions.

Dependence of the torsional rigidity of DNA on base composition

The Escherichia coli phage 434 repressor binds as a dimer to the operator of the DNA helix. Although the centre of the operator is not in contact with protein, the repressor binding affinity can be reduced at least 50-fold by changing the sequence there: operators with A.T base pairs near their centre bind the repressor more strongly than do operators with G.C base pairs at the same positions. To explain these observations, it has been proposed that the base composition at the centre of the operator affects the affinity of the operator for repressor by altering the ease with which operator DNA can undergo the torsional deformation necessary for complex formation. In this model, the variation in binding affinity would require the torsion constant to have specific values and to change in a sequence-dependent manner. We have now measured torsion constants for DNAs with widely different base compositions. Our results indicate that the torsion constants depend only slightly on the overall composition, and firmly delimit the range of values for each. Even the upper-limit values are much too small to account for the observed changes in affinity of the 434 repressor. These results rule out simple models that rely on substantial generic differences in torsion constant between A.T-rich sequences and G.C-rich sequences, although they do not rule out the possibility of particular sequences having abnormal torsion constants.

Dynamic bending rigidity of DNA

Rapidly relaxing components in the decay of the transient electric dichroism of DNA restriction fragments were reported by Diekmann et al. [(1982) Biophys. Chem. 15, 263-270] and Pörschke et al. [(1987) Biopolymers 26, 1971-1974]. These are analyzed using a new normal mode theory for weakly bending rods and assigned to bending. The longest bending relaxation times for fragments with 95-250 base pairs coincide with the theoretical curve calculated for a dynamic bending rigidity corresponding to a dynamic persistence length Pd = 2100 A. Analysis of the relative amplitudes of fast and slow components following weak orienting pulses is also consistent with a rather large dynamic persistence length. The enhancement of the relative amplitude of the fast component in large electric fields is attributed to steady-state bending of initially perpendicular DNAs by the field. Several reasons are proposed why the dynamic bending rigidity is 4 times larger than the apparent static bending rigidity inferred from equilibrium persistence length measurements on the same fragments.

Effects of chloroquine on the torsional dynamics and rigidities of linear and supercoiled DNAs at low ionic strength

The magnitude and uniformity of the torsion elastic constant (alpha) of linear and supercoiled pBR322 DNAs are measured in 3 mM Tris as a function of added chloroquine/basepair ratio (chl/bp) by studying the fluorescence polarization anisotropy of intercalated ethidium dye. The time-resolved FPA is measured using a picosecond dye-laser for excitation and time-correlated single-photon counting detection. For both linear and supercoiled DNAs, alpha remains uniform except at the very highest chl/bp ratio examined. For the linear DNA, alpha decreases from 5.0 x 10(-12) dyne-cm at chl/bp = 0 to about 3.5 x 10(-12) dyne-cm at chl/bp = 0.5, and remains at that value up to chl/bp = 5, whereupon it increases back up to its original value. For the supercoiled DNA, alpha remains constant at about 5.2 x 10(-12) dyne-cm from chl/bp = 0 up to chl/bp = 5, whereupon it increases in parallel with the linear DNA. The effect of chloroquine on the secondary structure, torsion constant, and torsional dynamics evidently differs substantially between linear and supercoiled DNAs, even under conditions where the supercoiled DNA is completely relaxed and both DNAs bind the same amount of dye. This strongly contradicts any notion that the local structures of linear and relaxed supercoiled DNA/dye complexes with the same binding ratio are identical. The increase in apparent alpha at chl/bp = 5 for both DNAs may be due to stacking of the chloroquine in the major groove and consequent stiffening of the filament.

Interaction of chloroquine with linear and supercoiled DNAs. Effect on the torsional dynamics, rigidity, and twist energy parameter

The magnitude and uniformity of the torsion elastic constant (alpha) of linear pBR322 DNA and supercoiled pBR322 DNAs with high-twist (sigma = -0.083) and normal-twist (sigma = -0.48) are measured in 0.1 M NaCl as a function of added chloroquine/base-pair ratio (chl/bp) by studying the fluorescence polarization anisotrophy (FPA) of intercalated ethidium dye. The time-resolved FPA is measured by using a picosecond dye laser for excitation and time-correlated single-photon counting detection. A general theory is developed for the binding of ligands that unwind superhelical DNAs, and the simultaneous binding of two different intercalators is treated in detail. The equilibrium constant (K) for binding chloroquine to linear pBR322 DNA and the number (r) of bound chloroquines per base pair are determined from the relative amplitude ratio of the slow (normally intercalated) and fast (free) components in the decay of the (probe) ethidium fluorescence intensity as a function of chl/bp. For chloroquine binding to supercoiled pBR322 DNAs, the intrinsic binding constant is assumed to be the same as for the linear DNA, but the twist energy parameter ET (N times the free energy to change the linking number from 0 to 1 in units of kBT) is regarded as adjustable. Using the best-fit ET, the binding ratios r are calculated for each chl/bp ratio. Twist energy parameters are also determined for ethidium binding to these supercoiled DNAs by competitive dialysis. For chloroquine binding, we obtain ET = 360 and 460 respectively for the normal-twist and high-twist supercoiled DNAs. For ethidium binding the corresponding values are ET = 280 +/- 70 and 347 +/- 50. Like other dye-binding values, these are substantially lower than those obtained by ligation methods. In the absence of chloroquine, the torsion constants of all three DNAs are virtually identical, alpha = (5.0 +/- 0.4) x 10(-12) dyn.cm. For linear pBR322 DNA, the magnitude and uniformity of alpha remain unaltered by intercalated chloroquine up to r = 0.19. This finding argues that the FPA is not significantly relaxed by diffusion of any kinks or solitons. If alpha d denotes the torsion constant between a dye and a base pair and alpha 0 that between two base pairs, then our data imply that alpha d/alpha 0 lies in the range 0.65-1.64, with a most probable value of 1.0.(ABSTRACT TRUNCATED AT 400 WORDS)

Melting of a self-complementary DNA minicircle. Comparison of optical melting theory with exchange broadening of the nuclear magnetic resonance spectrum

Melting curves are calculated for the 16-base-pair duplex DNA sequence 5' GTATCCGTACGGATAC 3' linked on the ends by TTTT single-strand loops. The equilibrium statistical thermodynamic theory of DNA melting is modified to include effects of end-loops on the melting transition. An excellent fit of the experimental melting curve in 0.2 M-NaCl is obtained using two adjustable parameters, one for end-loop formation and the other for formation of the complete 40-base single-strand loop. The best-fit calculated melting curve permits evaluation of these parameters. The free energy to close a TTTT end-loop is 2.12 kcal/mol (1 cal = 4.184 J). A TTTT end-loop or hairpin loop is significantly more stable than an internal loop of comparable size sandwiched between two helical regions, even after allowing for the different stacking contributions. Reasons for this increased stability are presented. The loop free energy of the 40-base single-strand open minicircle is evaluated to be +1.27 kcal/mol, thus favoring the melting of two end-loops into the large open minicircle. The present results are compared with those of others for d(T-A) oligomers. The sequence TTTT forms a more stable end-loop, or hairpin, than TATA by about 2.0 kcal/mol. Theoretical rate constants for the proton-transfer step in the standard hydrogen-exchange model are calculated by extending the theory of diffusion-controlled reactions to take account of the electrostatic potential of the DNA. The predicted ratios of rate constants for different pairs of catalysts exchanging an A.T proton agree satisfactorily with the available experimental data for a 14-base-pair linear duplex, which confirms the diffusion-control of the proton-transfer step. Data presented here for the 16 base-pair duplex of the minicircle are consistent with catalysis-limited exchange in which the proton-transfer step is likewise diffusion-controlled. Under catalysis-limited conditions, the imino proton exchange rates are predicted from the catalytic rate constants, prevailing buffer catalyst concentrations, and the equilibrium constants to form the unstacked open state of optical melting theory. The observed exchange rates of the A.T base-pairs show no sign of the strong predicted end-melting trend, and exceed the predicted values by factors of 10 to 400. Moreover, the succession of "melting" in the nuclear magnetic resonance line-broadening deviates from that predicted by optical melting theory.(ABSTRACT TRUNCATED AT 400 WORDS)

Change of conformation and internal dynamics of supercoiled DNA upon binding of Escherichia coli single-strand binding protein

The influence of Escherichia coli single-strand binding (SSB) protein on the conformation and internal dynamics of pBR322 and pUC8 supercoiled DNAs has been investigated by using dynamic light scattering at 632.8 and 351.1 nm and time-resolved fluorescence polarization anisotropy of intercalated ethidium. SSB protein binds to both DNAs up to a stoichiometry that is sufficient to almost completely relax the superhelical turns. Upon saturation binding, the translational diffusion coefficients (D0) of both DNAs decrease by approximately 20%. Apparent diffusion coefficients (Dapp) obtained from dynamic light scattering display the well-known increase with K2 (K = scattering vector), leveling off toward a plateau value (Dplat) at high K2. For both DNAs, the difference Dplat - D0 increases upon relaxation of supercoils by SSB protein, which indicates a corresponding enhancement of the subunit mobilities in internal motions. Fluorescence polarization anisotropy measurements on free and complexed pBR322 DNA indicate a (predominantly) uniform torsional rigidity for the saturated DNA/SSB protein complex that is significantly reduced compared to the free DNA. These observations are all consistent with the notion that binding of SSB protein is accompanied by a gradual loss of supercoils and saturates when the superhelical twist is largely removed.

Effect of Mg2+ on solution conformation of two different transfer ribonucleic acids

We have investigated the effect of Mg2+ on the solution conformation of two different tRNAs by studying the decay of the fluorescence polarization anisotropy of intercalated ethidium on a nanosecond time scale. In the presence of endogenous Mg2+, yeast tRNAPhe and Escherichia coli tRNAVal1 exhibit similar behavior; i.e., the fluorescence from the intercalated ethidium decays biexponentially with lifetimes of approximately 25 and approximately 5 ns, and the fluorescence polarization anisotropy decays with a lifetime of approximately 25 ns. However, once Mg2+ is removed from the two tRNAs, their behavior is no longer similar. In the case of yeast tRNAPhe, it appears that titrating with Mg2+ restores the tRNA to the condition that it was in prior to the Mg2+ removal. This is not so for E. coli tRNAVal1, in which case titrating with Mg2+ results in a two-component anisotropy decay with lifetimes of approximately 25 and approximately 6 ns. Rudimentary calculations indicate that the 6-ns component does not result simply from a change in conformation of the tRNA. However, torsional motions in the tRNA facilitated by a torsion "joint" with a rigidity approximately 1/40 that of intact linear phi 29 DNA would yield a decay component on this time scale with about the right amplitude. We are thus left with the possibility that (after initially removing magnesium) titrating tRNAVal1 with Mg2+ leads to increased internal flexibility and a significant amplitude of a deformational relaxation mode. At any rate, there is no question that after removal of Mg2+ tRNAPhe and tRNAVal1 display quite different solution conformation behavior. These findings are in qualitative agreement with recent 500-MHz 1H NMR results from solutions of these two tRNAs.

Rotational dynamics of transfer ribonucleic acid: effect of ionic strength and concentration

We have investigated the influence of ionic strength and nucleic acid concentration on the rotational Brownian motion of Escherichia coli tRNA1Val by studying the decay of the fluorescence polarization anisotropy (FPA) of intercalated ethidium on a nanosecond time scale. The rotational relaxation time tau R remains essentially constant as the ionic strength is varied from 2 to 100 mM at a tRNA concentration of 54 mg/mL. tau R also remains practically unchanged as the tRNA concentration is varied from 0.3 to 54 mg/mL at an ionic strength of 130 mM. Present hydrodynamic theories generally predict a more pronounced concentration dependence for rotational diffusion than we observe. This disagreement may result from a nonrandom distribution of the tRNA molecules in solution due to electrostatic interactions. By combining independent data from time-resolved nuclear Overhauser effect (NOE) cross-relaxation experiments and FPA experiments on the same tRNA, we are able to estimate the interproton spacing for the guanine N1-H and the uracil N3-H of the GU-50 base pair in E. coli tRNA1Val. This distance is 0.272 nm.

Structures and dynamics of a supercoiled DNA

Secondary structures of supercoiled (RF) M13mp7 DNA are investigated by time-resolved fluorescence polarization anisotropy, which monitors the magnitude and uniformity of the torsional rigidity. Tertiary structures are monitored by gel electrophoresis. Seven distinct long-lived structural conformers of this supercoiled DNA are identified: four result directly from different replicates of the same standard preparation procedure; one results from an alternate preparation; and two result from irreversible conversions of such forms to daughter products. These seven conformers all exhibit either of two different, but apparently uniform, torsional rigidities, depending upon the buffer type. These and other data imply that two different secondary structures can prevail in this supercoiled DNA and that neither is ordinary B helix. Each conformer also exhibits one of three basic gel mobilities. The observed dual secondary structures, metastability, and hysteresis of this DNA are shown to follow naturally, if the primary function of supercoiling is actually to facilitate remote control of gene activity by site-specific regulatory proteins. A specific model is proposed for gene regulation by protein control of remote junctions between secondary structure domains. The previously inexplicable stimulatory effect of the prmup-1 mutation in the right operator region of the lambda repressor is rationalized by certain aspects of this model.

Fluorescence depolarization and temperature dependence of the torsion elastic constant of linear phi 29 deoxyribonucleic acid

The torsion elastic constant alpha of linear phi 29 DNA has been determined as a function of temperature from 10 to 78 degrees C by studying the decay of the fluorescence polarization anisotropy (FPA) of intercalated ethidium dye. The time-dependent FPA was measured by using a picosecond dye laser for excitation and time-correlated single photon counting detection. Over the region 10-74 degrees C, alpha was effectively constant within experimental error, varying from (3.5 +/- 0.4) X 10(-12) dyn cm at 10 degrees C to (3.7 +/- 0.3) X 10(-12) dyn cm at 74 degrees C. At 78 degrees C, which is just above the melting temperature Tm = 76 degrees C, alpha decreased to (3.3 +/- 0.3) X 10(-12) dyn cm, and at 90 degrees C, where the DNA is completely denatured, both the fluorescence lifetime and the decay time of the FPA are characteristic of unbound ethidium bromide. The weak temperature dependence of alpha implies that DNA torsional deformations do not occur primarily at sites of high enthalpy perturbed structures such as open base pairs.